%0 Journal Article 
%A Klavžar, Sandi
%A Kuziak, Dorota
%A González Yero, Ismael
%T Further Contributions on the Outer Multiset Dimension of Graphs
%D 2022
%@ 1422-6383
%U http://hdl.handle.net/10498/29371
%X The outer multiset dimension dim ms(G) of a graph G is the cardinality of a smallest set of vertices that uniquely recognize all the vertices outside this set by using multisets of distances to the set. It is proved that dim ms(G) = n(G) - 1 if and only if G is a regular graph with diameter at most 2. Graphs G with dim ms(G) = 2 are described and recognized in polynomial time. A lower bound on the lexicographic product of G and H is proved when H is complete or edgeless, and the extremal graphs are determined. It is proved that dimms(Ps□Pt)=3 for s≥ t≥ 2.
%K grids
%K lexicographic product of graphs
%K outer multiset dimension
%K Outer multiset resolving set
%~ Universidad de Cádiz